If you see random application crashes, kernel panics, and failures in simple programs that have worked for a long time, it is possible you are experiencing RAM failure.
When RAM starts going bad, what you write to an address is not what you get back when you read it later. This causes random corruption of data, programs that crash, and even kernel "oops"es and kernel panics. If it's only a small amount of RAM that is corrupt then few programs will fail, but something will eventually fail when that memory gets used.
Some kernel panics may bring the system to a halt. If they reoccur soon after the system is off for a while you can be more confident it isn't a heat-related issue.
Even small programs may fail if they happen to use the affected memory. If they work once but then fail on a different attempt, this can be a sign of memory failure, since the memory used will be different from run to run.